24 boys out of 64 classmates is what percent

The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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Answer:

The answer is 20

Step-by-step explanation:

The wave starts at the origin and doesn't complete the cycle until unit 20.

Answer:

\(\displaystyle 20\)

Step-by-step explanation:

\(\displaystyle \boxed{y = cos\:(\frac{\pi}{10}x - \frac{\pi}{2})} \\ \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{5} \hookrightarrow \frac{\frac{\pi}{2}}{\frac{\pi}{10}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{20} \hookrightarrow \frac{2}{\frac{\pi}{10}}\pi \\ Amplitude \hookrightarrow 1\)

OR

\(\displaystyle \boxed{y = sin\:\frac{\pi}{10}x} \\ \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{20} \hookrightarrow \frac{2}{\frac{\pi}{10}}\pi \\ Amplitude \hookrightarrow 1\)

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of \(\displaystyle y = cos\:\frac{\pi}{10}x,\) in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted \(\displaystyle 5\:units\)to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD \(\displaystyle 5\:units,\)which means the C-term will be positive, and by perfourming your calculations, you will arrive at \(\displaystyle \boxed{5} = \frac{\frac{\pi}{2}}{\frac{\pi}{10}}.\)So, the cosine graph of the sine graph, accourding to the horisontal shift, is \(\displaystyle y = cos\:(\frac{\pi}{10}x - \frac{\pi}{2}).\)Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit \(\displaystyle [-15, 1],\)from there to \(\displaystyle [5, 1],\)they are obviously \(\displaystyle 20\:units\)apart, telling you that the period of the graph is \(\displaystyle 20.\)Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at \(\displaystyle y = 0,\)in which each crest is extended one unit beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

After tackling the differential equation, we get the common arrangement \(y = C_1e^{x\sqrt{-\frac{1}{30}\sec(3x)}} + C_2e^{-x\sqrt{-\frac{1}{30}\sec(3x)}}\), where C₁ and C₂ are self-assertive constants speaking to the specific solution's values.

To unravel the given homogeneous differential condition, we are able to follow these steps:

Step 1: Modify the condition in standard shape.

y'' + (1/30)sec(3x)y =

Step 2: Accept a solution of the shape

\(y = e^{rx}\), where r could be consistent to be decided.

Step 3: Calculate the primary and moment subordinates of y with regard to x.

\(y' = re^{rx\)

\(y'' = r^2e^{rx\)

Step 4: Substitute the expected arrangement and its subsidiaries into the differential condition.

\(r^2e^{rx} + \frac{1}{30}\sec(3x)e^{rx} =\)

Step 5: Isolate both sides of the condition by \(e^{rx\) to disentangle.

r² + (1/30)sec(3x) =

Step 6: Illuminate the coming about the quadratic condition for r².

r² = -(1/30)sec(3x)

Step 7: Take the square root of both sides to fathom for r.

\(r = \pm\sqrt{-\frac{1}{30}\sec(3x)\)

Step 8: Since we are searching for genuine arrangements, ready to center on the positive square root:

\(r = \sqrt{-\frac{1}{30}\sec(3x)\)

Step 9: The common arrangement is gotten by combining the two directly autonomous arrangements:

\(y = C_1e^{x\sqrt{-\frac{1}{30}\sec(3x)}} + C_2e^{-x\sqrt{-\frac{1}{30}\sec(3x)}}\)

where C1 and C2 are subjective constants.

Note: The answer may change depending on the particular conditions or starting values given for the differential condition.

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Equations b,c, and e accurately represent this statement.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

The three equation accurately represents this statement is;

4.9 x-(-3) = 12.8

3+ 4.9 x = 12.8

12.8 = 4.9 x +3

Hence, equations b,c, and e accurately represent this statement.

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Answer:

The answer is D

Step-by-step explanation:

When the exponent is negative then you go in to decimals

Answer:

since its a negative number you need to to go to the decimals> therefore the answer would be (D)

Answer:

y = 3/2x + 7

Step-by-step explanation:

If two lines are parallel to each other, they have the same slope.

The first line is 3x - 2y = 2. First, let's put this into standard form.

3x - 2y = 2

Add 2y to both sides to make y positive.

3x = 2y + 2

Subtract 2 from both sides to isolate y.

3x - 2 = 2y

Isolate y further by dividing both sides by 2.

3/2x - 1 = y or y = 3/2x - 1

This is now your first line. Its slope is 3/2. A line parallel to this one will also have a slope of 3/2.

Plug this value (3/2) into your standard point-slope equation of y = mx + b.

y = 3/2x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (-6, -2). Plug in the x and y values into the x and y of the standard equation.

-2 = 3/2(-6) + b

To find b, multiply the slope and the input of x (-6)

-2 = -9 + b

Now, add 9 to both sides to isolate b.

7 = b

Plug this into your standard equation.

y = 3/2x + 7

This equation is parallel to your given equation (y = 3/2x - 1) and contains point (-6, -2)

Hope this helps!

Answer

x=4

Explanation

-4 = x -8

add 8 to both sides

-4+8 = x

x=4

The maximum money supply with a 5% reserve requirement and a $400 initial deposit is $8,000.

To calculate the maximum total amount of money that will be in the money supply, we need to consider the money multiplier effect based on the reserve requirement.

The money multiplier is given by the formula: MM = 1 / reserve requirement.

Given that the reserve requirement is 5% (rr = 0.05), the money multiplier is MM = 1 / 0.05 = 20.

The initial deposit is $400.

To calculate the maximum total amount of money in the money supply, we multiply the initial deposit by the money multiplier:

Maximum Money Supply = Initial Deposit * Money Multiplier

= $400 * 20

= $8,000.

Therefore, the maximum total amount of money that will be in the money supply is $8,000 when the reserve requirement is 5% and all currency is deposited in banks with no excess reserves.

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Answer:

Step-by-step explanation:

B being the midpoint of AC means:

AB = BC = 0.5AC  

AB = 0.5AC  ⇒  AC = 2AB

AC = 2(62 - 7) = 2×55 = 110

Answer:

hope this helps :)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

complement angle meabs 90° so,

90° - 48°

= 42°

hence the complement angle of 48° is 42°

Step-by-step explanation:

x -y = 92     x = 92+y

xy = minumum

(92+y)  * y  = minumum

y^2 + 92y  = minumum      this quadratic has a minimum at

                                               y = -b/2a =  - 92/(2*1) = - 46

x -  -46 = 92   shows x = +46         minimum is then - 2116  

The total surface area of the trapezoidal prism is S = 3,296 inches²

Given data ,

Let the total surface area of the trapezoidal prism is S

Now , the measures of the sides of the prism are

Side a = 10 inches

Side b = 32 inches

Side c = 10 inches

Side d = 20 inches

Length l = 40 inches

Height h = 8 inches

Lateral area of prism L = l ( a + b + c + d )

L = 40 ( 10 + 32 + 10 + 20 )

L = 2,880 inches²

Surface area S = h ( b + d ) + L

On simplifying the equation , we get

S = 2,880 inches² + 8 ( 52 )

S = 3,296 inches²

Hence , the surface area of prism is S = 3,296 inches²

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Answer:

Translation as Triangle A has been translated by vector (3,-1) to now being (-2,-3)

Translation as Triangle A has been translated by a vector (3,-1) to now being (-2,-3).

The process of changing the location of the image on the coordinate system will be known as the translation.

A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have merely changed their direction or directions.

Given that Translate Triangle A by a vector (3, -1) to give triangle B. Then, rotate your triangle B 180° around the origin to give triangle C.

Triangle A translation ⇒ (3,-1)

The second translation = (-2,-3).

Therefore, the translation as Triangle A has been translated by a vector (3,-1) to now being (-2,-3).

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Answer:

Step-by-step explanation:

S = 4πr²

First of all divide both sides by 4π

That's

Find the square root of both sides in order to isolate r

That's

We have the final answer as

Hope this helps you

Answer:

75

Step-by-step explanation:

mean = average so add up all your numbers, then divide by the amount of numbers so

46 + 56 + 64 + 64 + 72 + 76 + 77 + 82 + 94 + 96 + 99 = 826

826 ÷ 11 = 75.09 (about)

A health professional shortage area (HPSA) is a "region with insufficient numbers of health care providers", as described in option C.

A HPSA is an area, whether rural or urban, with a shortage of primary medical care, dental or mental health providers. This is determined based on the ratio of healthcare providers to the population, as well as other factors such as income levels and health outcomes.

HPSAs are designated by the Health Resources and Services Administration (HRSA) and are prioritized for federal funding and programs to help address the shortage. This designation helps to identify areas where access to healthcare is limited, and to encourage healthcare providers to practice in those areas.

HPSAs can also be further categorized into subtypes, such as primary care, dental, or mental health HPSAs, to better target interventions and resources. Option C is correct.

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The equation of a line through (2, -7) that is parallel to 2x + 5y = 20 is 2x + 5y = -24.

The equation of a line through (2, -7) that is perpendicular to 2x + 5y = 20 is 5x - 2y = -19.

To find the equation of a line parallel to a given line, we need to know that parallel lines have the same slope. The given equation, 2x + 5y = 20, can be rewritten in slope-intercept form as y = (-2/5)x + 4. From this form, we can determine that the slope of the given line is -2/5.

Since parallel lines have the same slope, we can use the slope-intercept form and substitute the coordinates (2, -7) into the equation y = (-2/5)x + b to find the y-intercept. Plugging in the values, we have -7 = (-2/5)(2) + b. Simplifying this equation, we get -7 = -4/5 + b, and by solving for b, we find that b = -24/5.

Substituting the determined slope (-2/5) and y-intercept (-24/5) into the slope-intercept form, we get the equation of the line parallel to 2x + 5y = 20 as 2x + 5y = -24.

To find the equation of a line perpendicular to the given line, we need to know that perpendicular lines have negative reciprocal slopes. The negative reciprocal of -2/5 is 5/2.

Using the point-slope form y - y₁ = m(x - x₁), where (x₁, y₁) represents the point (2, -7) and m represents the slope, we substitute the values to get y - (-7) = (5/2)(x - 2). Simplifying, we have y + 7 = (5/2)x - 5, and by rearranging the equation, we find the equation of the line perpendicular to 2x + 5y = 20 as 5x - 2y = -19.

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Answer:

7√3

Step-by-step explanation:

Answer:

(negative infinity, 4]

Step-by-step explanation:

Reminder: the range is all the possible y values the function can get by plugging in x values.

Since this is a downward opening parabola, it won't have a lower boundary, which means that the answer must be (negative infinity, 4]

We can further check that's correct by seeing that the parabola has its vertex at 4, which is written in the answer.

That means the correct answer must be (negative infinity, 4]

Answer:

30

Step-by-step explanation:

Answer

Area = 80.11 cm^2 and perimeter = 39.99 cm

Step-by-step explanation:

The area of each small sector

= (60/360) * π *  r^2

= (60/360) * π * 6^2

= 1/6 * 36 * π

= 6π

So the area of the 2 small sectors = 12π cm^2

Area of the large sector

= 1/6 * π * 9^2

= 13.5 π

Total area = 25.5π cm^2.

= 80.11 cm^2

Perimeter = 6 + 6 + 3 + 3 + 2 small arcs + 1 large arc

= 18 + 2 * 1/6 * 2πr + 1/6 * 2πr

= 18 + 2/3π*6 + 1/3π*9

= 18 + 7π

= 39.99 cm.

The structure of 12-crown-4 is shown below.

12-Crown-4, also known as lithium ionophore V and 1,4,7,10-tetraoxacyclododecane, is a crown ether with the chemical formula C8H16O4. It is a lithium cation-specific cyclic tetramer of the chemical compound ethylene oxide.

12-crown-4 combines with alkali metal cations, similar to other crown ethers. It has a strong selectivity for the lithium cation due to the cavity diameter of 1.2–1.5.

LiClO4 can be used as a template cation in a modified Williamson ether synthesis to create 12-Crown-4:

(CH2CH2O)4 + 2 NaCl + 2 H2O = (CH2OCH2CH2Cl)2 + (CH2OH)2 + 2 NaOH

In the presence of gaseous boron trifluoride, it can also result from the cyclic oligomerization of ethylene oxide.

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Answer:

2 solutions

Step-by-step explanation:

y = - 2x + 3 → (1)

y = x² - 6x + 3 → (2)

substitute y = x² - 6x + 3 into (1)

x² - 6x + 3 = - 2x + 3 ( subtract - 2x + 3 from both sides )

x² - 4x = 0 ← factor out x from each term on the left side

x(x - 4) = 0

equate each factor to zero and solve for x

x = 0

x - 4 = 0 ⇒ x = 4

substitute these values into (1)

x = 0 : y = - 2(0) + 3 = 0 + 3 = 3 ⇒ (0, 3 )

x = 4 : y = - 2(4) + 3 = - 8 + 3 = - 5 ⇒ (4, - 5 )

the 2 solutions are (0, 3 ) and (4, - 5 )

Answer:

(5yz)^2(x^2z^3)

(25y^2z^2)(x^2z^3)

25x^2y^2z^5

Step-by-step explanation:

To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.

1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:

V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49

We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:

V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)

Here is a more detailed explanation of the substitution:

In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.

When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3

In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.

When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)

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